# 1-(Future values )For each of the cases shown in the following table,

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1-(Future values )For each of the cases shown in the following table, calculate the future value of the single cash flow deposited today that will be available at the end of the deposit period if the interest is compounded annually at the rate specified over the given period.

Case             Single cash flow                Interest rate               Deposit period (years)

A                  \$ 200                                 5%                                 20
B                   4,500                                8                                    7
C                  10,000                               9                                   10
D                  25,000                              10                                   12
E                   37,000                             11                                     5
F                   40,000                             12                                     9

2-(Present values)For each of the cases shown in the following table, calculate the present value of the cash flow, discounting at the rate given and assuming that the cash flow is received at the end of the period noted.

Case              Single cash flow               Discount rate       End of period (years)

A                    \$ 7,000                            12%                        4
B                     28,000                             8                            20
C                    10,000                            14                            12
D                    150,000                          11                              6
E                     45,000                           20                              8

3-(Future value of an annuity)Future value of an annuity For each case in the accompanying table, answer the questions that follow.

Amount of                 Interest                       Deposit period
Case          annuity                          rate                          (years)

A               \$ 2,500                         8%                               10
B                 500                            12                                 6
C                30,000                        20                                 5
D                11,500                        9                                   8
E                 6,000                        14                                  30

a. Calculate the future value of the annuity assuming that it is
(1) An ordinary annuity.
(2) An annuity due.
b. Compare your findings in parts a(1) and a(2). All else being identical, which type
of annuity—ordinary or annuity due—is preferable? Explain why.

4-(Present value of an annuity) Consider the following cases.

Case                     Amount of annuity          Interest rate             Period (years)

A                          \$ 12,000                           7%                            3
B                            55,000                           12                             15
C                            700                               20                              9
D                           140,000                          5                                7
E                            22,500                          10                               5

5-(Bond valuation—Annual interest) Calculate the value of each of the bonds shown in the following table, all of which pay interest annually.

Bond           Par value        Coupon interest rate         Years to maturity          Required return
A                 \$1,000             14%                                  20                             12%
B                   1,000              8                                     16                               8
C                   100               10                                      8                               13
D                   500               16                                     13                              18
E                   1,000             12                                     10                              10

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